2 citations · 3 across the 5 of their papers we have counts for
5 papers
Matrix similarity transformations derived from extended -analogues of the Toda equation and Lotka-Volterra system
R. Watanabe, M. Shinjo, M. Iwasaki
The -Toda equation is derived from replacing ordinary derivatives with -derivatives in the famous Toda equation. In this paper, we associate an extension of the -Toda equa…
Application of the extended -discrete Toda equation to computing eigenvalues of Hessenberg totally nonnegative matrices
R. Watanabe, M. Shinjo, Y. Yamamoto +1
The Toda equation is one of the most famous integrable systems, and its time-discretization is simply the recursion formula of the quotient-difference (qd) algorithm for computing…
Two characteristic polynomials corresponding to graphical networks over min-plus algebra
Sennosuke Watanabe, Yuto Tozuka, Yoshihide Watanabe +2
In this paper, we investigate characteristic polynomials of matrices in min-plus algebra. Eigenvalues of min-plus matrices are known to be the minimum roots of the characteristic p…
Discrete-time analysis for the integrable discrete Toda equations and the discrete Lotka-Volterra system
Masato Shinjo, Yoshimasa Nakamura, Masashi Iwasaki +1
The discrete autonomous/non-autonomous Toda equations and the discrete Lotka-Volterra system are important integrable discrete systems in fields such as mathematical physics, mathe…
An asymptotic expansion of the Casorati determinant and its application to discrete integrable systems
Masato Shinjo, Masashi Iwasaki, Yoshimasa Nakamura
The Hankel determinant appears in the representation of solutions to several integrable systems. Asymptotic expansion of the Hankel determinant thus plays a key role for investigat…